Schmidt问题的有限类似及其变式
On Finite Analogs of Schmidt's Problem and Its Variants
摘要：
我们完善施密特的问题和分区身份有关的2色分区，我们将称为Uncu-Andrews-Paule定理。我们将使用Boulet-Stanley权重和Berkovich-Warnaar的Rogers-SzegIgnolynomials公式来处理这个问题，并提出各种Schmidt问题定理及其改进。我们的新Schmidt型结果包括使用偶数索引部分的和，部分的交替和，钩长以及奇数索引部分的和出现在原来的Schmidt问题。我们还翻译了一些施密特的问题，类似的关系，加权分区计数与乘法权重的罗杰斯-拉马努金分区。
英文摘要：
We refine Schmidt's problem and a partition identity related to 2-color partitions which we will refer to as Uncu-Andrews-Paule theorem. We will approach the problem using Boulet-Stanley weights and a formula on Rogers-Szegő polynomials by Berkovich-Warnaar, and present various Schmidt's problem alike theorems and their refinements. Our new Schmidt type results include the use of even-indexed parts' sums, alternating sum of parts, and hook lengths as well as the odd-indexed parts' sum which appears in the original Schmidt's problem. We also translate some of our Schmidt's problem alike relations to weighted partition counts with multiplicative weights in relation to Rogers-Ramanujan partitions.
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